# -*- Mode: shell-script -*-
#############################################################################
##
#A  trans9.grp                  GAP group library            Alexander Hulpke
#A                                                              & Greg Butler
#A                                                               & John McKay
##
##
#Y  Copyright (C) 2018-2021, Carnegie Mellon University
#Y  All rights reserved.  See LICENSE for details.
#Y  
#Y  This work is based on GAP version 3, with some files from version 4.  GAP is
#Y  Copyright (C) (1987--2021) by the GAP Group (www.gap-system.org).
##
##  This file contains the transitive groups of degree 9.
##
##


TRANSGRP[9]:=[
[(1,2,3,4,5,6,7,8,9),"C(9) = 9"],
[(1,2,9)(3,4,5)(6,7,8),(1,4,7)(2,5,8)(3,6,9),"E(9) = 3[x]3"],
[(1,2,3,4,5,6,7,8,9),(1,8)(2,7)(3,6)(4,5),"D(9) = 9:2"],
[(1,2,9)(3,4,5)(6,7,8),(1,2)(4,5)(7,8),
(1,4,7)(2,5,8)(3,6,9),"S(3)[x]3"],
[(1,2,9)(3,4,5)(6,7,8),(1,4,7)(2,5,8)(3,6,9),
(1,2)(3,6)(4,8)(5,7),"S(3)[1/2]S(3) = 3^2:2"],
[(1,4,7)(2,8,5),(1,2,3,4,5,6,7,8,9),"1/3[3^3]3"],
[(1,2,9)(3,4,5)(6,7,8),(1,4,7)(2,5,8)(3,6,9),
(3,4,5)(6,8,7),"E(9):3 = [3^2]3"],
[(1,2,9)(3,4,5)(6,7,8),(1,2)(4,5)(7,8),
(1,4,7)(2,5,8)(3,6,9),(3,6)(4,7)(5,8),"S(3)[x]S(3) = E(9):D_4"],
[(1,2,9)(3,4,5)(6,7,8),(1,4,7)(2,5,8)(3,6,9),(1,8,2,4)(3,5,6,7),"E(9):4"],
[(1,4,7)(2,8,5),(1,2,3,4,5,6,7,8,9),(1,8)(2,7)(3,6)(4,5),"[3^2]S(3)_6"],
[(1,2,9)(3,4,5)(6,7,8),(1,4,7)(2,5,8)(3,6,9),
(3,4,5)(6,8,7),(1,2)(3,6)(4,8)(5,7),"E(9):6 = 1/2[3^2:2]S(3)"],
[(3,4,5)(6,8,7),(1,4,7)(2,5,8)(3,6,9),(3,6)(4,7)(5,8),"[3^2]S(3)"],
[(1,2,9)(3,4,5)(6,7,8),(1,4,7)(2,5,8)(3,6,9),
(3,4,5)(6,8,7),(1,2)(3,5)(6,7),"E(9):D_6 = [3^2:2]3 = [1/2.S(3)^2]3"],
[(1,2,9)(3,4,5)(6,7,8),(1,4,7)(2,5,8)(3,6,9),
(1,8,2,4)(3,5,6,7),(1,6,2,3)(4,7,8,5),"M(9) = E(9):Q_8"],
[(1,2,9)(3,4,5)(6,7,8),(1,4,7)(2,5,8)(3,6,9),(1,6,4,5,2,3,8,7),"E(9):8"],
[(1,2,9)(3,4,5)(6,7,8),(1,4,7)(2,5,8)(3,6,9),
(1,2)(3,5)(6,7),(1,8)(2,4)(5,7),"E(9):D_8"],
[(1,2,9),(1,4,7)(2,5,8)(3,6,9),"[3^3]3 = 3 wr 3"],
[(1,2,9)(3,4,5)(6,7,8),(1,4,7)(2,5,8)(3,6,9),
(3,4,5)(6,8,7),(1,2)(3,6)(4,8)(5,7),(1,2)(3,5)(6,7),
"E(9):D_12 = [3^2:2]S(3) = [1/2.S(3)^2]S(3)"],
[(1,2,9)(3,4,5)(6,7,8),(1,4,7)(2,5,8)(3,6,9),
(1,6,4,5,2,3,8,7),(1,2)(3,5)(6,7),"E(9):2D_8"],
[(1,2,9),(1,4,7)(2,5,8)(3,6,9),(3,6)(4,7)(5,8),"[3^3]S(3) = 3 wr S(3)"],
[(1,2,9),(1,4,7)(2,5,8)(3,6,9),(1,2)(3,6)(4,8)(5,7),"1/2.[3^3:2]S(3)"],
[(1,2,9),(1,2)(4,5)(7,8),(1,4,7)(2,5,8)(3,6,9),"[3^3:2]3"],
[(1,2,9)(3,4,5)(6,7,8),(1,4,7)(2,5,8)(3,6,9),
(1,8,2,4)(3,5,6,7),(3,4,5)(6,8,7),"E(9):2A_4"],
[(1,2,9),(1,2)(4,5)(7,8),(1,4,7)(2,5,8)(3,6,9),
(3,6)(4,7)(5,8),"[3^3:2]S(3)"],
[(1,2,9),(4,5)(7,8),(1,4,7)(2,5,8)(3,6,9),"[1/2.S(3)^3]3"],
[(1,2,9)(3,4,5)(6,7,8),(1,4,7)(2,5,8)(3,6,9),
(1,6,4,5,2,3,8,7),(3,4,5)(6,8,7),"E(9):2S_4"],
[(1,9)(2,3)(4,5)(6,7),(1,2,4,3,6,7,5),
(2,5)(3,6)(4,7)(8,9),"L(9) = PSL(2,8)"],
[(1,2,9),(1,2),(1,4,7)(2,5,8)(3,6,9),"[S(3)^3]3 = S(3) wr 3"],
[(1,2,9),(4,5)(7,8),(1,4,7)(2,5,8)(3,6,9),(3,6)(4,7)(5,8),
"[1/2.S(3)^3]S(3)"],
[(1,2,9),(4,5)(7,8),(1,4,7)(2,5,8)(3,6,9),
(1,2)(3,6)(4,7)(5,8),"1/2[S(3)^3]S(3)"],
[(1,2,9),(1,2),(1,4,7)(2,5,8)(3,6,9),(3,6)(4,7)(5,8),
"[S(3)^3]S(3) = S(3) wr S(3)"],
[(1,9)(2,3)(4,5)(6,7),(1,2,4,3,6,7,5),
(2,5)(3,6)(4,7)(8,9),(2,4,6)(3,5,7),"L(9):3 = P|L(2,8)"],
[(1,8,9),(2,8,9),(3,8,9),(4,8,9),(5,8,9),(6,8,9),(7,8,9),"A(9)"],
[(1,9),(1,2),(2,3),(3,4),(4,5),(5,6),(6,7),(7,8),"S(9)"]];

TRANSPROPERTIES[9]:=
[[9,0,1,1,[F,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,T],
[3009],[7009],[3,8009]],
[9,0,1,1,[F,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F],
[3009],[7009],[3003,7009]],
[18,0,1,1,[F,F,F,T,F,F,F,F,F,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,T],
[3009],[-3018],[-2018,-3,2009]],
[18,0,1,-1,[F,F,T,F,F,F,F,F,F,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,T,F,F,F,F],
[-1009,-18],[-2018,-1009],[-2018,-1009,-6,-3,3]],
[18,0,1,1,[F,F,F,T,F,F,F,F,F,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F],
[3009],[-3018],[-3018,-3003]],
[27,0,1,1,[F,F,F,F,F,F,F,F,T,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,T],
[9,27],[1009,1027],[3,2027],[4,[1009,3027]]],
[27,0,1,1,[F,F,F,F,F,F,F,F,T,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F],
[9,27],[1009,1027],[3,1027,2009]],
[36,0,1,-1,[F,F,T,T,F,F,F,F,F,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,T,F,F,F,F],
[-1009,-18],[-1018,36],[-1018,-1003,-6,36]],
[36,1,1,1,[F,F,F,T,F,F,F,F,F,F,T,F,F,F,F,F,T,F,F,F,F,F,F,F,F,F,F,F,F],
[-1018],[-1036],[-1036,1006]],
[54,0,1,1,[F,F,F,T,F,F,F,F,T,F,T,F,F,F,F,F,F,F,F,F,F,F,F,T,F,F,F,F,T],
[9,27],[-54,-18],[-54,-3,27],[4,[-54,-18,1027]]],
[54,0,1,1,[F,F,F,T,F,F,F,F,T,F,T,F,F,F,F,F,F,F,F,F,F,F,F,T,F,F,F,F,F],
[9,27],[-54,-18],[-54,-18,-9,-3]],
[54,0,1,-1,[F,F,T,F,F,F,F,F,T,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,T,F,F,F,F],
[-9,27],[-1009,-54],[-2009,-54,-3]],
[54,0,1,-1,[F,F,T,F,F,F,F,F,T,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,T,F,F,F,F],
[-9,27],[-18,1027],[-18,3,9,1027]],
[72,1,2,1,[F,F,F,T,F,F,F,F,F,F,T,F,F,F,F,F,T,F,F,F,F,F,F,F,F,F,F,F,F],
[36],[72],[12,72],[4,[-2018,72]]],
[72,1,2,-1,[F,F,F,T,F,F,F,F,F,F,T,F,F,F,F,F,T,F,F,F,F,F,F,F,F,F,F,T,F],
[-36],[-72],[-72,12],[29,[-1036]],[4,[-72,-36,-18]]],
[72,1,1,-1,[F,F,T,T,F,F,F,F,F,F,T,F,F,F,F,F,T,F,F,F,F,F,F,F,T,F,F,F,F],
[-1018],[-1036],[-1036,-1006]],
[81,0,1,1,[F,F,F,F,T,F,F,F,T,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,T],
[9,27],[1009,1027],[3,2027],[4,[27,81,1009]]],
[108,0,1,-1,[F,F,T,T,F,F,F,F,T,F,T,F,F,F,F,F,F,F,F,F,F,F,F,T,T,F,F,F,F],
[-9,27],[-54,-18],[-54,-18,-9,-3]],
[144,1,2,-1,[F,F,T,T,F,F,F,F,F,F,T,F,F,F,F,F,T,F,F,F,F,F,F,F,T,F,F,T,F],
[-36],[-72],[-72,12],[29,[72]],[4,[-72,-36,-18]]],
[162,0,1,-1,[F,F,T,F,T,F,F,T,T,F,T,F,F,F,F,F,F,F,F,F,F,F,T,F,T,F,F,F,T],
[-9,27],[-1009,-54],[-54,-27,-3]],
[162,0,1,1,[F,F,F,T,T,F,F,F,T,F,T,F,F,F,F,F,F,F,F,F,F,F,F,T,F,F,F,F,T],
[9,27],[-54,-18],[-54,-3,27],[4,[-81,-18,27]],[9182,[-54,-18,1027,2009]]],
[162,0,1,-1,[F,F,T,F,T,F,F,F,T,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,T,F,F,F,T],
[-9,27],[-18,1027],[-27,3,1027],[29,[1009],[27],[27]]],
[216,1,2,1,[F,F,F,T,F,F,F,F,T,F,T,F,F,F,F,F,T,F,F,F,F,F,F,T,F,F,F,F,F],
[36],[72],[12,72],[4,[54,72]]],
[324,0,1,-1,[F,F,T,T,T,F,F,T,T,F,T,F,F,F,F,F,F,F,F,F,F,F,T,T,T,F,F,F,T],
[-9,27],[-54,-18],[-54,-27,-3],[9182,[-2009,-1054,-18]]],
[324,0,1,1,[F,T,F,F,T,F,T,F,T,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,F,T],
[9,27],[18,1027],[3,2027]],
[432,1,2,-1,[F,F,T,T,F,F,F,F,T,F,T,F,F,F,F,F,T,F,F,F,F,F,F,T,T,F,F,T,F],
[-36],[-72],[-72,12],[4,[-72,54]]],
[504,1,3,1,[F,F,F,T,F,F,F,F,F,F,T,F,F,F,F,F,F,F,F,F,F,F,F,F,F,T,F,F,T],
[36],[72],[84],[2362,[252,2126]]],
[648,0,1,-1,[T,T,T,F,T,T,T,F,T,T,T,F,F,F,F,F,F,F,F,F,F,F,F,F,T,F,F,F,T],
[-9,27],[-18,1027],[-27,3,1027],[29,[18],[27],[27]]],
[648,0,1,-1,[F,T,T,F,T,F,T,T,T,F,T,F,F,T,F,F,F,F,F,F,F,F,T,F,T,F,F,F,T],
[-9,27],[-54,18],[-54,-27,-3]],
[648,0,1,1,[F,T,F,T,T,F,T,F,T,F,T,F,T,F,F,T,F,F,F,F,F,F,F,T,F,F,F,F,T],
[9,27],[-54,-18],[-54,-3,27],[4,[-81,-18,27]],[9182,[-108,-18,2009]]],
[1296,0,1,-1,[T,T,T,T,T,T,T,T,T,T,T,F,T,T,F,T,F,F,F,F,F,F,T,T,T,F,F,F,T],
[-9,27],[-54,-18],[-54,-27,-3],[9182,[-2009,-108,-18]]],
[1512,1,3,1,[F,F,F,T,F,F,F,F,T,F,T,F,F,F,F,F,F,F,F,F,F,F,F,T,F,T,F,F,T],
[36],[72],[84],[2362,[252,378]],[10094,[[14,1056]]]],
[181440,1,7,1,[F,T,F,T,T,F,T,F,T,F,T,F,T,F,F,T,T,T,F,T,T,F,F,T,F,T,F,F,T],
[36],[72],[84],[2362,[252,378]],[10094,[[56,70]]]],
[362880,1,9,-1,[T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T,T],
[-36],[-72],[-84]]];

